Catalysis of the Hydrolysis of Internal Alpha Peptide Bonds in a Polypeptide Chain by a Catalytic Mechanism That Involves a Catalytic Triad Consisting of a Serine Nucleophile That Is Activated by a Proton Relay Involving an Acidic Residue (e.g. Aspartate or Glutamate) and a Basic Residue (usually Histidine).